Dynamic modeling and fuzzy compensation sliding mode control for two-inertia rotation system with flexible structure

In fields such as on-orbit maintenance robotic arms and electric driving systems, the two-inertia rotating system with flexible structure (TIRS-FS) has received increasing attention due to its lightweight and flexibility. Flexible structures are prone to elastic deformation during motion, which poses a significant challenge to the dynamic modeling and high-precision control of the TIRS-FS. This paper presents a comparative analysis of three simplified TIRS-FS dynamics models. Based on the more accurate dynamics model obtained, the fuzzy compensated sliding mode control method is proposed to achieve accurate control of the TIRS-FS. Firstly, the TIRS-FS is discretized using the assumed modal method. Then, using the Lagrange equation, the dynamical equations considering the two-dimensional (2D) deformation of the flexible structure and the joint-driven friction are established. Additionally, fuzzy rules are utilized to approximate and compensate for the uncertainty terms present in the TIRS-FS dynamical equations. These fuzzy systems are then combined into a control law. Finally, through simulation analysis and control experiments, it is demonstrated that the proposed control method can effectively achieve accurate control of the TIRS-FS.